altmann2010_poroelasticity.ipynb

{
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  "metadata": {
    "colab": {
      "name": "altmann2010-poroelasticity.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNVcf4LZcxZZ9xWroqlRjqf",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/yohanesnuwara/computational-geophysics/blob/master/altmann2010_poroelasticity.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-vdXWM6yjaLC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-9WMECuAjyj3",
        "colab_type": "text"
      },
      "source": [
        "Radius to reservoir from wellbore ranging from 0 to 500 m, in a sandstone reservoir"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hqCAMH9vj4z7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 613
        },
        "outputId": "df7d3511-6591-462b-b60f-b87931b3f179"
      },
      "source": [
        "r = np.arange(0, 5010, 10) # radius, m\n",
        "year = 1\n",
        "t = year * (3.154E+7) # time, seconds in year\n",
        "\n",
        "# knowns from Altmann paper\n",
        "\n",
        "Kd = 12 # drained bulk modulus, GPa\n",
        "Kg = 40 # grain bulk modulus, GPa\n",
        "G = 5.5 # shear modulus, GPa\n",
        "Kf = 2 # fluid bulk modulus, GPa\n",
        "rhof = 1000 # fluid density, kg/m3\n",
        "poro = 0.167 # porosity of sandstone\n",
        "g = 9.8 # gravitational acceleration, m/s2\n",
        "kf = 0.1E-6 # hydraulic conductivity, m/s\n",
        "\n",
        "# Gassmann fluid substitution, according to Altmann\n",
        "Ku = (Kg + (Kd * (poro * (Kg / Kf) - poro - 1))) / (1 - poro - (Kd / Kg) + (poro * (Kg / Kf)))\n",
        "print('The undrained (saturated) bulk modulus:', Ku, 'GPa')\n",
        "\n",
        "# Biot-Willis coeff\n",
        "alpha = 1 - (Kd / Kg)\n",
        "print('The Biot-Willis coefficient:', alpha)\n",
        "\n",
        "# Lame parameter lambda\n",
        "lame_lambda = Kd - (2 * G / 3)\n",
        "\n",
        "# undrained Lame parameter lambda\n",
        "lame_lambda_u = Ku - (2 * G / 3)\n",
        "\n",
        "# stress path defined by Engelder & Fischer (1994), assume infinite reservoir\n",
        "v = lame_lambda / (3 * Kd - lame_lambda)\n",
        "sp = alpha * ((1 - 2 * v) / (1 - v))\n",
        "print('Stress path at infinite time and infinite reservoir:', sp, '\\n')\n",
        "\n",
        "# diffusivity\n",
        "k = kf / (g * rhof)\n",
        "numerator = (lame_lambda_u - lame_lambda) * (lame_lambda + 2 * G)\n",
        "denominator = (alpha**2) * (lame_lambda_u + 2 * G)\n",
        "c = k * ((numerator / denominator) * 1E+9) # GPa to Pa, multiply by 1E+9\n",
        "print('Diffusivity:', c, 'm2/s')\n",
        "\n",
        "# boltzmann variable (dimensionless)\n",
        "boltz = r / np.sqrt(c * t)\n",
        "\n",
        "# error function\n",
        "errf = scipy.special.erf(0.5 * boltz)\n",
        "errfc = 1 - errf\n",
        "g_func = errf - ((1 / np.sqrt(np.pi)) * boltz * np.exp(-0.25 * (boltz**2)))\n",
        "\n",
        "# spatio-temporal radial stress path\n",
        "A = (2 * alpha * G) / (lame_lambda + 2 * G)\n",
        "B = 1 + ( ((2 / boltz**2) * g_func) / (errfc) )\n",
        "\n",
        "stress_path_radial = A * B\n",
        "\n",
        "# plot stress path\n",
        "plt.figure(figsize=(10,7))\n",
        "p1 = plt.plot(r, stress_path_radial, color='blue')\n",
        "p2 = plt.plot([0, max(r)], [sp, sp], '--', color='red')\n",
        "plt.legend((p1[0], p2[0]), (['Spatio-temporal stress path (Altmann et al, 2010)', 'Stress path at infinite (Engelder and Fischer, 1994)']))\n",
        "plt.title('Reservoir Stress Path', size=20, pad=10)\n",
        "plt.xlabel('Radius from wellbore (m)', size=15)\n",
        "plt.ylabel('$\\Delta \\sigma_r / \\Delta P$', size=15)\n",
        "plt.xlim(0, max(r))\n",
        "plt.ylim(0, 1.5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "The undrained (saturated) bulk modulus: 17.060676478182287 GPa\n",
            "The Biot-Willis coefficient: 0.7\n",
            "Stress path at infinite time and infinite reservoir: 0.3982758620689654 \n",
            "\n",
            "Diffusivity: 0.08352374587295491 m2/s\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:52: RuntimeWarning: divide by zero encountered in true_divide\n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:52: RuntimeWarning: invalid value encountered in multiply\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 1.5)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 88
        },
        {
          "output_type": "display_data",
          "data": {
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GDh2ablvPnj1p2bJlum1jx47l0UcfDXmuomjfvn0888wzeX5fbq7bgAEDqF+/PhEREQwZ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\nhMFOkiSpJgx2kiRJNWGwkyRJqon/D+foZ4RRTmWEAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 720x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}